> I´m asking myself is it makes any sense to go on...
Please continue to post your images. They are a welcome source of color
and intricate, though-provoking shapes during these dreary winter months!
Now that I have Factory Restored my computer, I hope to try DOSBOX
fairly soon, and calculate some images based on yours, too.
I know that there are others out there who are viewing your images -- in
a more passive sort of way -- they're just not "jumping up and down" and
celebrating them very loudly...
- Hal Lane
########################
# hallane(a)earthlink.net
########################
-----Original Message-----
From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Albrecht Niekamp
Sent: Tuesday, January 19, 2016 5:32 PM
To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com>
Subject: [Fractint] Jazz - Unversal Fractal V2 (Phoenix Inside3)
Jazz - Unversal Fractal V2 (Phoenix Inside3) ; There has been hardly any response (except Hal) this year so far and I´m asking myself is it makes any sense to go on (not for the first time).
Some time ago Jim (has anyone heard from him ??) performed a survey to find out if there is still some interest. The response was not so bad but he did not return anyway. Now I´m asking you to mail a short note again in order to decide. Thank you!
;
The UF V2 has gained a lot more complexity compared to the first version. It is almost impossible to find a spot without zooming adventures, so it´s hard to decide where to stop.
Featured today are 5 Images (out of 50 sofar), and the diversity is amazing. Which one is your favorite ?
;
;
https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93…
;
Path: MultifracArchive/New/Newgif
Image 65-69
Path: MultifracArchive/New/Newpar\NEW.PAR
;
Albrecht
Das Wort für Welt ist Wald
_______________________________________________
Fractint mailing list
Fractint(a)mailman.xmission.com
https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
---
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus
Jazz - Unversal Fractal V2 (Phoenix Inside3)
;
There has been hardly any response (except Hal)
this year so far and I´m asking myself is it makes
any sense to go on (not for the first time).
Some time ago Jim (has anyone heard from him ??)
performed a survey to find out if there is still
some interest. The response was not so bad but he did
not return anyway. Now I´m asking you to mail a short
note again in order to decide. Thank you!
;
The UF V2 has gained a lot more complexity compared
to the first version. It is almost impossible to find
a spot without zooming adventures, so it´s hard to
decide where to stop.
Featured today are 5 Images (out of 50 sofar), and the
diversity is amazing. Which one is your favorite ?
;
;
https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93…
;
Path: MultifracArchive/New/Newgif
Image 65-69
Path: MultifracArchive/New/Newpar\NEW.PAR
;
Albrecht
Das Wort für Welt ist Wald
Rebirth
;
This is an image from 10 years ago,
one of my alltime favorites,
created with the first MFR_10 version.
I never managed to recreate it with later
versions, so here is the original again
in a 16/9 aspect at 1280/1024, in addition
a subtle modification, maybe you have an
idea what I did to it.
;
https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93…
;
Path: MultifracArchive/New/Newgif
Image 61
Path: MultifracArchive/New/Newpar\NEW.PAR
;
Albrecht
---------- JoTz wrote: ----------
> As I'm having a slight problem with the email to this group , I
> I shall attempt to send to you.
I interpret this to mean that I should post this to
the [Fractint] list. Done.
I have some concern about the email systems and / or list
serve software involved reformatting the layout of the text...
I don't think I've seen characters thrown away -- just lines
re-formatted so they become less easy to read.
Re what JoTz's equations are modeling:
> The circuit [simulation] supposedly generates a
> rectified sine wave [over time];
> . . .
> The equation is a second order , very stiff
> non linear differential equation...
- Hal Lane
########################
# hallane(a)earthlink.net
########################
From: sciwise(a)ihug.co.nz [mailto:sciwise@ihug.co.nz]
Sent: Sunday, January 10, 2016 10:15 PM
To: Hal Lane <hallane(a)earthlink.net>
Subject: RE: [Fractint] Tedious formula
Hi Hal,
As I'm having a slight problem with the email to this group , I
I shall attempt to send to you.
I might be able to replace the exp with temp*temp.
To be really accurate exp() is what's used , however to
get a general idea as to what's going on your recommendation
has merit.
I tried setting the initial (x,y) to (0,0) , I managed to get a
few more iterations , however the overflow problems
remain.
Setting (p,h) to a small value provides a few more iterations,
however the output isn't quite what I expected ; I may need
to use a circuit simulator , like TopSpice to determine what
the output is meant to look like.
The equation is a second order , very stiff non linear differential
equation ,
I haven't been able to find an analytical solution to this
upon the internet.
You're right about the reuse of x and y , however the
first (x,y) values are outside the main loop also this type
of coding isn't different from the Volterra Lotka formula
file that comes standard with Fractint.
I'm fairly certain that alteration of (x,y) within the main
loop is correct.
Nevertheless I shall try your recommendation.
The q value is reused , within the main loop , however
I'm not expecting any difficulty in doing so ; however I
can also change that.
The variable t1 is an independent time variable , used
when calculating the value of sin() ; the input function.
I'm now pondering how I might do a two loop iteration
within Fractint ; can't figure out how it might be done.
The circuit supposedly generates a rectified sine wave ;
however I really need to look at the circuit simulator results.
This is all a bit of a jigsaw puzzle.
I'm including my formula file for the diode model as this
illustrates how I dealt with the exp() term in a simpler instance.
======== START PARAMETER FILE=======================================
Diode {
reset=1821 type=formula formulafile=c:\winf1821\alndgh.frm
formulaname=LnDioGH
corners=-0.16588419/0.25978091/-0.15031315/0.1691023 float=y
maxiter=512 logmap=yes
colors=00000j0j0jj0j00j0j0jjkkkkrkdmwW000W0WW000WW0W0WWFNF<5>zNFFVF<5>zV\
FFbF<5>zbFFjF<5>zjFFrF<5>zrFFzF<5>zzFFFN<5>zFNFNN<5>zNNFVN<5>zVNFbN<5>zb\
NFjN<5>zjNFrN<5>zrNFzN<5>zzNFFV<5>zFVFNV<5>zNVFVV<5>zVVFbV<5>zbVFjV<5>zj\
VFrV<5>zrVFzV<5>zzVFFb<5>zFbFNb<5>zNbFVb<5>zVbFbb<5>zbbFjb<5>zjbFrb<5>zr\
bFzb<5>zzbFFj<5>zFjFNj<5>zNjFVj<5>zVjFbj<5>zbjFjj<5>zjjFrj<4>rrjzywccdWW\
Wz000z0zz000zz0z0zzzzz
}
comment {
From :
sciwise(a)ihug.co.nz July 2009
copyright c 2009
This is a model of a diode , as an electronic
component .
It utilizes Newton's method to solve a non-linear
equation ; known as the ideal diode or Shockley equation .
The very basic form of this equation is :
i = Ids*(exp(Vs/(n*Vt))-1)
where ,
Q = 1.6*(10^-19) Electronic Charge .
K = 1.38*(10^-23) Boltzman's constant .
T = Absolute Temperature , in Kelvins .
T = 273 [K] + degreesC
For degreesC = 25 , Vt ~= 0.025 [v]
Ids = Saturation current .
Vs = Applied , source , voltage .
n = Ideality factor = ( 1 to 2 ) .
Vt = K * T / Q Thermionic Voltage .
A more realistic model of a diode will include the finite
ohmic resistance of the leads .
A parallel conductance is also modeled , as this speeds
the convergence of Newton's method .
Therefore the circuit we're modelling looks like this .
i -->
----------------------------,
' |
| -------------------,
| | .---.
Vs - D --- | | Gm
--- /_\ |___|
| |__________________|
| |
| .---.
| | | Rs
| |___|
'----------------------------'
Where D is represented by the ideal diode equation .
Now the total current , i , flowing through this
circuit is :
i = Ids*(exp((Vs-i*Rs)/(n*Vt))-1) + Gm*(Vs-i*Rs)
This equation needs to be solved in terms of i and
be put in a form that can be readily and accurately
solved through Newton's method .
The steps involved are :
1)
Let log(x) = (Vs-i*Rs)/(n*Vt)
2)
Solve log(x) = (Vs-i*Rs)/(n*Vt) in terms of i .
i = -(n*Vt*log(x)-Vs)/Rs
3)
Substitute the expression for i , from (2) into
i = Ids*(exp((Vs-i*Rs)/(n*Vt))-1) + Gm*(Vs-i*Rs)
-(n*Vt*log(x)-Vs)/Rs = Ids*(x-1) + Gm*(Vs--((n*Vt*log(x)-Vs)/Rs)*Rs)
-(n*Vt*log(x)-Vs)/Rs = Ids*(x-1) + Gm*((n*Vt*log(x)/Rs)*Rs)
(Vs-n*Vt*log(x))/Rs = Ids*(x-1) + Gm*(n*Vt*log(x))
4)
Solve (3) for x ,
x = -((Gm*n*Rs*Vt+n*Vt)*log(x)-Vs-Is*Rs)/(Is*Rs),Is*Rs,1);
5)
Find the derivative of (4) in terms of x .
1 = -(Gm*n*Rs*Vt+n*Vt)/(Is*Rs*x)
6)
Now Newton's iteration formula is :
x = x - f(x) / f '(x) , where f '(x) == d
f(x) / dx .
7)
For this example :
f(x) = x
= -((Gm*n*Rs*Vt+n*Vt)*log(x)-Vs-Is*Rs)/(Is*Rs),Is*Rs,1)
and
f '(x) = 1 = -(Gm*n*Rs*Vt+n*Vt)/(Is*Rs*x)
8)
Therefore Newton's iteration formula for this example is :
x = x - ( -((Gm*n*Rs*Vt+n*Vt)*log(x)-Vs-Is*Rs)/(Is*Rs),Is*Rs,1) -
x )/( -(Gm*n*Rs*Vt+n*Vt)/(Is*Rs*x)-1)
9)
Simplifying (8)
x = x -( (-Ids*Rs-Vs)*x + Ids*Rs*x*x + (n+Gm*n*Rs)*Vt*x*log(x) ) /
( (n + Gm*n*Rs)*Vt+Ids*Rs*x )
Substitute
u = Gm*n*Rs*Vt+n*Vt
vr = Ids*Rs
x = x-( -(Vs+vr)*x + vr*x*x + u*x*log(x) )/(vr*x+u))
In this logarithmic format overflow , and possibly underflow , is
avoided .
10 )
We need to be able to convert x back to i , to do this we use the
inverse of the original
substitution :
log(x) = (Vs-i*Rs)/(n*Vt)
Solving for i ,
i = - ( log(x)*(n*Vt) - Vs ) / Rs
Substitute
Pt = n*Vt
i = - ( log(x)*Pt - Vs ) / Rs
Between successive iterations of Newton's formula
the previous value of i is compared with the present,
if the absolute difference is less than a predefined
tolerance , Pd , then the iteration stops .
Vs is a complex voltage source , possibly equivalent
to a multi phase voltage source .
This is a basic diode model and doesn't include the
effects of diode junction capacitance .
For small voltages a purely exponential representation
of the diode model may converge quicker than the
logarithmic and still remain accurate .
The logarithmic model has been implemented as a BASIC
language program and compared with data from a SPICE
simulation , for a real voltage source , there is
good agreement .
For a Complex voltage source , the few samples
generated from the BASIC program are in good agreement
with those from MAXIMA CAS .
}
frm:LnDioGH{
;
;
; Complex Voltage - Complex Current
; Diode Characteristics .
;
; for 1N4148 silicon type .
; Level 1 model .
;
; at 25 degrees C
;
;
Pd = (10^(-13)),
Gm = 9.4*(10^(-13)),
Ids = 2.52*(10^(-09)),
Rs = 0.968,
n = 1.752,
Vt = 0.025,
u = Gm*n*Rs*Vt+n*Vt,
Pt = n*Vt,
vr = Ids*Rs,
Vs = Pixel,
x = (0.1,0),
x = x-((u*x*log(x)+vr*x*x-(Vs+vr)*x)/(vr*x+u)),
y = -(Pt*log(x)-Vs)/Rs,
tol = (1,0):
u = y;
x = x-((u*x*log(x)+vr*x*x-(Vs+vr)*x)/(vr*x+u));
y = -(Pt*log(x)-Vs)/Rs,
tol = |u-y|,
tol > Pd
}
comment {
The floating point option needs to be selected ,
512 iterations , or more , should be selected .
Also a logarithmic palette .
Minibrot structures aren't immediately apparent at
the default parameter settings .
A parameter setting of :
xmin - 0.005770310598 xmax - 0.005666943901
ymin 0.000516417395 ymax 0.000594104392
shows embedded minibrots and spirals , weather this
is relevant in a real diode is unknown .
You might be able to locate minibrots elsewhere on
the map .
}
========END PARAMETER FILE==================
----------------------------------------------------------------------
On 10/01/2016 17:08, Hal Lane wrote:
----------------------------------------------------------------------
> Your tidy up is good...
Thanks.
> ...I'm using maxima cas...
Very good!
Here are a few more wild and crazy debugging ideas:
[exp] grows quite large after one or two iterations...
Here's an odd idea. Could you temporarily replace the
exp with a function that doesn't grow so quickly -- just
to get some results to look at? Perhaps a power?
So, instead of:
q = exp( s*a1*x )
you could try something like:
temp = s*a1*x
q = temp * temp
or:
temp = s*a1*x
q = temp * temp * temp * temp
q would then grow (or shrink for "temp" values less
than one,) but not in such a violent way. Using even
numbers of "temp" multiplied together always makes
its sign always be positive -- like the result of an exp().
What does the physics of the RLC circuit say about the
use of the exp() ?
I'm also wondering if the initial x and y are meant to be 0 and 0 and v =
(x,y) .
That's certainly easy to try -- but the significance of
doing this ought to be thought about, as well.
Here's an odd observation -- x and y get used for two
different purposes:
z = pixel
x = real(z)
y = imag(z)
and also:
c = x+h*(u+b)
d = y + h*(w + s*a1*b*b + s*b2*q*b + s*b3*b + b2*q*v + b1*q + s*b1)
x = c
y = d
z = x*x + y*y
Might the 2nd place where x and y are used need to
be xtemp and ytemp? It looks like the values of x and y
possibly needing to be constant during the calculation
of a pixel might be getting compromised by their
reuse -- unless that re-usage is intentional,
Also, I note that q is used in two different calculations:
This re-usage may or may not be intentional...
q = exp(s*a1*x )
. . .
q = exp(s*a1*a )
Note that the color map could be useful for debugging
when you get to the stage where you're looking at
resultant images.
Perhaps you could have a map that has big color
changes in adjacent lower values to be able to
better see what is going on in the initial iterations.
Is the image supposed to somehow visually depict
the ringing of a diode-clamped RLC circuit?
- Hal Lane
########################
# hallane(a)earthlink.net
########################
------------------------Original Message------------------------
From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of
sciwise(a)ihug.co.nz
Sent: Saturday, January 9, 2016 5:50 PM
To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com>
Subject: Re: [Fractint] Tedious formula
-------------------------------------------------------------------------
Your tidy up is good , for some reason I was having difficulty
with negative exponents.
Presently I'm using maxima cas to look at the values that exp(q)
takes , and indeed it grows quite large after one or two iterations;
to such an extent that maxima runs out of digits when printing.
Without going into the details of the underlying equations , I
encountered a similar difficulty a number of years ago when I wrote
LnDioGH.frm ; do a web search you should be able to find the code.
I'm also wondering if the initial x and y are meant to be 0 and 0 and v =
(x,y) .
=============================================
On 10/01/2016 03:52, Jonathan Osuch wrote:
On Sat, 2016-01-09 at 16:28 +1300, sciwise(a)ihug.co.nz
[1]wrote:
=============================================
Difficulties remain , however this is a slightly
improved version. For some reason the loop is exited after the first
iteration ; I'm starting to think that the exponential function exp(q) might
be the cause.
It depends upon what you are trying to iterate
during each loop. Take a
look at the following. I cleaned up the code
a little, but it still
doesn't work. DiodeRLC float=y { f =
1/real(p1)
z = pixel x = real(z) y = imag(z) p = 0.39757 h =
0.71743
s = -1 R = 1 L =0.001 C1 = 10^(-6) KT =
((1.3806485279) * 10^(-23)) * 270
twopi = 2 * pi q1 =
(1.602176620898) * 10^(-19)
Id = 10^(-12) a1 = q1/(KT) b1 =
(KT)/(q1*C1*L)
b2 = (KT)/(Id*q1*L) b3 = R/L t1 = 0 : v =
100*sin(twopi*t1)
q = exp( s*a1*x ) u = y w = s*a1*y*y + s*b2*q*y
+ s*b3*y + b2*q*v + b1*q + s*b1
a = x+p*u b = y+p*w q = exp(
s*a1*a )
c = x+h*(u+b) d = y + h*(w + s*a1*b*b + s*b2*q*b + s*b3*b +
b2*q*v + b1*q + s*b1)
x = c y = d t1 = t1 + f z = x*x + y*y t1
< maxit ; loops until t1 is >= maxit
}
Jonathan
Links:
------
[1] mailto:sciwise@ihug.co.nz
[2]
mailto:Fractint@mailman.xmission.com
[3]
https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
_______________________________________________
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https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
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---
This email has been checked for viruses by Avast antivirus software.
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-------------- JoTz said: -----------
> Please post to the list server.
Done.
Please see JoTz comments and link below.
- Hal Lane
########################
# hallane(a)earthlink.net
########################
From: LLOYD GARRICK [mailto:lgarr@colorado-hiking.net]
Sent: Sunday, January 10, 2016 1:04 PM
To: Hal Lane <hallane(a)earthlink.net>; Albrechtx_Multifract!!! <Multifrac(a)t-online.de>; Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com>
Subject: Re: [Fractint] Bemmsemaph
Here is all of Niekamp's images in the "new.par" rendered at 1024x768 for all who want but still have trouble running fractint [I guess noone had much success with my FractintOS? :( ]:
http://www.fractal-animation.net/an.zip
it's about 18Meg, 59 images
.
Please post to the list server
------------------- On January 9, 2016 at 9:24 PM ------------------
-------------------Hal Lane <hallane(a)earthlink.net> wrote: -----
Albrecht, this series (58, 59, 60) is a nice balance of
detail vs larger structure on multiple size scales. Nice
colors, too. 59 and 60 have striking, unusual large
scale features.
58 is a more familiar overall "Medusa-like" shape, but
set in an unusually-detailed background.
In 59, the dark gold colors next to the greens is very
pleasant.
To me, the bold, arched legs in 60 are very commanding.
Green and gold together are (again) pleasant.
- Hal Lane
########################
# hallane(a)earthlink.net
########################
----Original Message-----
From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Albrecht Niekamp
Sent: Saturday, January 9, 2016 5:42 PM
To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com>
Subject: [Fractint] Bemmsemaph
Bemmsemaph
;
The is the next step to more complextity:
Inside3 has been changed from Newton to
Phoenix, my nonsymmetrical version with
P1 input, not used sofar.
This version of the Universal Fractal also contains a mandel- not the minibrot -, due to Phoenix, with all it´s complexity.
;
https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93…
;
Path: MultifracArchive/New/Newgif
Images 58, 59, 60
Path: MultifracArchive/New/Newpar\NEW.PAR
;
Albrecht
Das Wort für Welt ist Wald
_______________________________________________
Fractint mailing list
Fractint(a)mailman.xmission.com
https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
---
---
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus
I'm attempting to construct a formula .
However there's
something amiss ; hence I'm seeking some
help on this from the group.
This is the formula :
comment{
Series Circuit .
(c) copyright
2016
sciwise(a)ihug.co.nz
Edward.Q.Montague
}
DiodeRLC {
f =
1/real(p1)
z = pixel
x = real(z)
y = imag(z)
p = 0.039757
h =
0.071743
s = -1
R = 1
L =0.001
C = 10^6
C = 1/C
K = 10^23
K =
(1.3806485279)/K
twopi = 6.283185307179586
T = 270
q = 10^19
q =
(1.602176620898)/q
Id = 10^12
Id = 1/Id
a1 = q/(K*T)
b1 =
(K*T)/(q*C*L)
b2 = (K*T)/(Id*q*L)
b3 = R/L
t1 = 0:
v = twopi*t1
v =
100*sin(w)
q = s*a1*x
q = exp( q )
u = y
w = s*a1*y*y + s*b2*q*y +
s*b3*y + b2*q*w + b1*q + s*b1
a = x+p*u
b = y+p*w
q = s*a1*a
q =
exp( q )
c = x+h*(u+b)
d = y + h*(w + s*a1*b*b + s*b2*q*b + s*b3*b +
b2*q*v + b1*q + s*b1)
x = c
y = d
t1 = t1 + f
z = x+flip(y)
|y|
Bemmsemaph
;
The is the next step to more complextity:
Inside3 has been changed from Newton to
Phoenix, my nonsymmetrical version with
P1 input, not used sofar.
This version of the Universal Fractal also
contains a mandel- not the minibrot -,
due to Phoenix, with all it´s complexity.
;
https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93…
;
Path: MultifracArchive/New/Newgif
Images 58, 59, 60
Path: MultifracArchive/New/Newpar\NEW.PAR
;
Albrecht
Das Wort für Welt ist Wald
